Weather Prediction and the Prospect for their Improvement
By
professor Vilhelm Bjerknes
Three articles written in Danish in the Norwegian newspaper Aftenposten 8-10 January 1904
I. The main task of meteorology
After closer examination, the thought of the future is hiding behind our struggle for
knowledge. As much as possible we want to lift the curtain which rests over things to come in
order to adjust our present activities accordingly.
One extensive knowledge about the future has gone into our blood completely. Without
offering deeper thoughts, we take our precautions related to the fixed variations of the time of
the day and the seasons. With faith in the relative stability of the society, we give our children
education which makes them competent citizens of a society of the same kind as our present
one. But in other directions special expertise is required, business men’s to judge the
conjunctions of business life, doctor’s for in a case of sickness to make diagnosis and
prognosis, all with the thought at present to do what is serving to our best in the future.
Our ability to consider future incidents, completely depend on integrated experience of earlier
incidents of the same kind. Studies of what has elapsed in the past, namely historical research,
always form the basis. Research has this historical nature even in experimental sciences,
where the scientist himself set up the experiments, which outcome he describes. And
oppositely, those sciences which direct goal is the study of the past as such, i.e. the historical
sciences in a more restricted sense, the history of mankind and the geological history of the
earth, has as their most distant and highest goal the thought of an understanding of the
continuous development from the past, trough the present towards the future.
A modern science, which more directly than most others deals with the future, is the
meteorology. It has simply attained in its objection the prediction of future weather.
The importance of reliable weather prediction is clear. The daily stories of losses of human
lives at sea we all know. The Swedish sea insurance companies alone, yearly disburse at least
more than 5, and probably close to 9 millions kroner in loss reimbursements. Because of
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reinsurance it is difficult to decide the accurate number. What a fully efficient and fully
reliable gale prediction system could achieve to reduce these numbers, all of us realise. Even
greater importance, state-economically considered, a perfect weather prediction system would
have for the mother mission of the civilised mankind, agriculture. Its cost would be for
nothing to count against the sum of all benefit it would do. The organisation of a weather
prediction system as perfect as possible is thus, philanthropically and state-economically
considered, as task of the greatest importance.
The meteorology has also already achieved a lot. This is recognised in the nicest way e.g. by
the English coast and fishing population. When the gale warnings were stopped for a while
after the death of the first pioneer, admiral FizRoy, they were restarted after a more perfect
system after eager requests from a large amount of coastal locations. And when it was realised
that more sea accidents took place on Mondays than on other days in the week, the gale
warning service was extended to Sundays because of pressure from the coastal communities.
For easily understandable reasons the farmer is more difficult to satisfy than the sailor. But for
anyone who from a neutral point of view pays attention, and not with the annoyance that a
single wrong prediction might provide, let themselves be leaded to rejection of the total
system, the benefit of the present daily weather forecasts is also evident for the farmer.
It is, however, equally certain that the system is not perfect. Before the predictions could be
issued far more completely, with precise account of the time of a weather change and the
duration of the new weather, and before they have gained broad confidence, they will not
obtain their whole benefit neither on land nor at sea. The feeling of the distance between what
has been obtained and what ought to be obtained, seems also to have exerted a paralyzing
effect on more than one meteorologist, who has gone tired under the stressing work with the
eternally changing temper of the weather.
But this kind of setbacks is phenomena of intermediary nature. They are obvious sign on, that
we from the beginning not have been entirely armed for the struggle, and that we must look
for new weapons. The prediction of what will be coming is in the end the highest goal of any
science, and for the meteorology it is, when all comes to all, not a draw-back, but an
invaluable privilege that its highest scientific task falls so close together with a practical task
of this importance. It is this extended goal, which must not be lost in sight, if the meteorology
is not to stagnate as a science. Any serious meteorological research effort gives its
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contribution to the final solution of this future task, all from the statistics made by
climatologists to studies of each spiralling storm by the dynamicists.
Against this background, weather prediction as the main task of meteorology, we will
examine a little closer what should be done in order to solve the task with the means which
we at present are holding.
II. Weather signs and the meteorologists’ present method for weather
forecasts
Weather prophets have always existed, and the belief in different weather signs is widespread. Many of these are completely without value. Others are signs of present weather
without any connection to what will come. These signs bear out as often as the prediction
“same weather today as tomorrow”, and this is often true, since the number of weather
changes in a year is substantially less than the number of days. When we in our mountain
communities thus will hear, that when a rainbow is showing up, there will be “small weather”,
i.e. frequent change between rain and sunshine, we immediately realise the self-deception.
The fact that sunbeams are reflected in raindrops, has in itself no influence on the coming
weather. It means simply that the “small weather” already is present, and that the “small
weather” has its tendency to persist like any other kind of weather.
There also exist, however, signs of higher value. Examples are the well known proverbs from
eastern Norway (Østlandet) “eastern clearing, wet cap” and “western clearing long lasting”,
which thus say that a clearing from east is an unreliable sign which soon will be followed by
precipitation, while a clearing from west promises nice weather for a longer period. They are
reliable signs, but have yet a local significance only. In western Norway opposite rules are
valid.
There is no main difference between the better weather signs like these and those after which
the meteorologists make their prognoses, like there is no main difference found between
laymen’s observations and scientific observations, between common sound thinking and
scientific thinking. But the meteorologist has firstly more resources, he does not take his
starting-point in a single clearing over a single hill, but reports from a large amount of
stations, which make him able to draw synoptical maps, which in a revealing way show the
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state of the atmosphere over a larger part of the earth. Secondly, he has available a larger
amount of critically proved experiences, on which the prognoses are built.
In reality there is a short distance between the mentioned proverbs and one of the
meteorologists’ fundamental laws. I will not include all interacting factors, but a main point is
the following: The eastern Norway elevates from the Swedish lowland up towards to the
Norwegian mountain range. The air masses brought in with easterly winds, will thus steadily
be lifted upwards, the more they approach the mountain range. Oppositely, the air masses,
which westerly winds bring across the mountain range, in its continuous motion glide
downwards. If the rule is rewritten: ascending airstream cause rain, descending air clear
weather, then we in all its simplicity have one of the fundamental laws of meteorology
between the connection the air motion and the distribution of clear weather or rain.
It is not always that simple, however, that one from the topography of a land might draw
conclusions on whether the air masses, which are brought over our heads, at the same time
ascend or descend. Here the barometer observations will help. Experience shows, that the air
down here at the earth flows towards those places where the barometer stands low, and out
from them, where it stands high. If one includes some partly very uncertain experience about
the laws after which barometric maxima and minima moves over the surface of the earth, then
we in a short sum have indicated the main points in the system of weather signs, after which
the meteorologists nowadays predict clear weather or rain, calm or gale.
That these forecasts might fail, we all know, and we need not go far to find cases where the
meteorology with its present resources would stand more or less helpless. The northernmost
Norway is in winter one the stormiest places on earth, and the total national accidents, which
from time to time take place, when large parts of the fishing fleet with crew and equipment go
under, is just far too well known. A glance at the climatological conditions at once shows the
reason for the frequency of the storms. On the basis of the climate tables of Mohn, Ekholm
has showed that the mean temperature in January at the outside islands in Lofoten is 27
degrees Celsius higher than the average for the same latitude around the earth. It is the effect
of the warm water of the Gulfstream. At the same time Sibirian winter coldness reigns further
in over the Finmark plateau. With other words, the nature has here placed an enormous damp
cattle side by side with a vast condenser. This damp engine must always work, and so it does
with huge irregular strokes.
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But just here, inside the work engine, which forms the storms, the issue of gale warnings,
after the current system of the meteorology, would bring forward the very largest difficulties.
The barometer readings at the different stations would give very incomplete results, since
according to investigations by Aksel S. Steen, almost half of the storms in Finmark take place
without being followed by any characteristic barometer drop. The stations, distributed along a
narrow stripe, would not give any overview. And above all, the engine sometimes works with
such a speed, that the gale warnings, based on compilation and treatment of barometer
observations, not could be spread in time.
III The extension of meteorological observations to higher air level and to
the ocean
That the meteorology might fail, even when it works under favourable conditions, and stand
more or less helpless on such tasks as the prediction of the storms in Finmark, is not
surprising. It is rather more surprising that it with present resources can achieve as much as it
does.
The duty of the meteorology is exactly of the same kind as that of a doctor, when he shall
predict the future course of a decease. The doctor first examines the present state of the
patient, makes the diagnosis, and on this he builds the prediction of the coming state, makes
the prognosis. If the prognosis is built on an incomplete diagnosis, it more or less depends on
shear luck if it proves true. The same must be the case for a meteorological prognosis, as long
as it is built on an utmost incomplete diagnosis of the state of the atmosphere.
What importance it would have for weather prediction in the northern European countries, if
weather telegrams from the northern Atlantic could be obtained, is sufficiently often
emphasized. The question of a telegraph cable to the Faroe Islands and Iceland have for this
reason been in question for long time. But another shortage is felt even more critical. All
observations are now taken down at the surface of the earth. But the rain comes from above.
With other words, it will be more important to know the state of the air at higher levels, where
the rain comes from, than here below, where we face it. The study of the higher air levels has
also progressed as the means to make observations have advanced.
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Knowledge about the motion of higher air layers is easiest to obtain. It might be found by
measuring the height and the speed of the clouds. In this direction Clement Lev,
Hildebrandsson, Ekholm and Hagstrøm, Helm Clayton and others have been working. In 1897
international cloud observations were made from a large number of stations throughout the
world. This has given us extended knowledge about the motion of the air, but not yet resulted
in practical applications in the interest of daily weather forecasting. But the time to make
cloud observations practically useable, is already here as I later will show.
Balloon trips for meteorological purposes have also been well known for long time, and lately
also the application of unmanned balloons, carrying self-registering instruments, have been
introduced. The manned balloons reach, with great danger for the life of the air skippers, to
heights like 10 000 meter, which is about the height of the highest clouds, the cirrus clouds.
Balloons with registrations have, however, reached more than the double of this height. In
order to obtain more complete results than those the isolated trips might give, one has also
organised simultaneous soundings of manned and unmanned balloons. These international
balloon trips, where several of the larger European countries participate, are now taken once a
month. Also this gives hope for extended common knowledge on the atmospheric conditions
at greater heights. But daily international balloon trips would be a too expensive and too
awkward an arrangement for daily weather prediction.
Still another means of measurement has been found, and this is for time being the one which
seems to be most promising. All of us know the paper kite, a toy which is widespread all over
the world. In particular the Malaysians are famous for their eagerness and skill in setting up
kites. The practical Americans have been in the front of taking this lovely toy into the service
of science. Just like a balloon, the kite might lift self- registering instruments into the air. But
of course, instruments with a value of several hundred krones can not be entrusted any kind of
a kite. Those who have set up an ordinary paper-kite, will remember its peculiar motions
when the wind is a little fresh. It shifts abruptly from side to side, as the tale twists like a
snake. If the tale is shortened, the motions will become more violent, and at last it will be
thrown around, for either like a raptor be casted towards the ground, or also to make a
complete loop in a wild dance in a circling track.
A kite with such disruptions can of course not be used, and even the best means for making it
stable, i.e. the tale, must be abandoned. It hinders the sounding to reach a greater height, and
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if another kite with a tail is set in further down to help carrying the weight of the line, the tail
will unavoidably wind around the line, and everything fails. Accordingly, the meteorological
kite must stand steady in the air without a tail. To a certain degree this situation is fulfilled by
the Malay kite, which is essentially the same as our toy kite, just with more fortunate choice
of conditions. But in strong wind it is still not sufficiently reliable. Uncountable tests have
been made to find better constructions, and the best results are until now generally obtained
with kites of the so-called Hargrave-type, due to the Australian inventor within the art of
flying, Hargrave. But the construction work of kites is not finished, and new progress is still
to come. Nevertheless, already the present kites give astonishing results.
With five or six kites in a row, the lowest ones to carry the line, a string of hardened steel
(piano string), and a suitable little motor to drag the system down again, it must now be
regarded as an easy matter to reach heights of two to three thousand meter above the ground.
Under appropriate conditions kites have already lifted instruments to a height of 5000 meter,
but the limit has probably not been reached. It is not unthinkable, that e.g. twice that height
might be reached, i.e. the same as the manned balloons. Then, with help of instruments, lifted
by kites, the whole cloud-carrying layer of the atmosphere might be examined. And the use of
kites will not be limited to days with wind. Even in complete calm weather, kites could easily
be lifted from a steamship or a motorboat.
Of fixed stations in aeronautical meteorology, Blue Hill at Boston might be specially
mentioned. It is founded by the wealthy American A. Lawrence Rotch, who must be
considered as the pioneer for application of kites in meteorology. In greater scale the topic
was first set up in Europe by the prosperous L. Teisserene de Bort, who also is known for
introducing unmanned register-balloons, and who has founded a station for his experiments in
Trappes close to Paris. An institute for aeronautical meteorology, which works with generous
allocations from the state, has already in several years been running in Berlin under leadership
of professor Assman. And a smaller station is found in Hamburg under professor Kløppen.
These two stations have already started to publish and distribute telegraphically daily
observations from higher air levels. Among larger efforts in aeronautic meteorology the
French-Scandinavian station must be mentioned, running in Jutland under leadership of
Teisserene de Bort, Hildebrandsson and Adam Paulsen. They succeeded in keeping
registering instruments aloft without major breaks in half a year. But most important for the
future will be the organisation of future kite-trips from several stations. Along this direction
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Weather Bureau in Washington made an interesting experiment as early as in 1898, when 17
lightly equipped kite stations were operating during the whole summer. What then proved to
be possible, will now function far more easily and with better security.
In addition to the fixed kite stations on land, floating stations at sea can also be applied. The
navigation of a kite is as easy, or even easier, from a steamship than from a land station. The
highest sounding from a ship so far, to 3900 meter, was obtained at the French-Scandinavian
station. Already at the hydrographical-biological congress in Stockholm in 1899, it was
decided that the hydrographical expeditions four times a year, for investigation of the northern
European ocean, should bring meteorological kites. This plan will hopefully soon come true,
and material of great value will surely be gained. Furthermore, tests with meteorological kites
have lately been performed from transatlantic steamship liners. And the thought has been
brought up, with help of wireless telegraphy to include these invaluable stations among those
that send daily weather reports in the interest of weather prediction.
IV Mechanics and physics, helping sciences for the meteorology
The technical task to provide observations from any part of the atmosphere, at the surface or
aloft, over sea or over land, must thus for the most part be considered as solved. And all
stations will, with help of the customary or the wireless telegraphy, be able to deliver daily
telegrams in the interest of weather prediction. What is left is the organisation, so that the
work which now is done from scattered initiative, can make its complete utilization, and next
the successive extension of the system as the demand acquires. When this organization work
is finished is just a question of time. And that situation might accordingly be realized at any
time, that the meteorologists get access to all the material which reasonably can be demanded
for their forecasts. This question then comes: Will the meteorologists, with access to this
material, be able to make the diagnosis of the immediate state of the atmosphere and the
prognosis of the future development of this state?
This question is not entirely meteorological. All the atmospheric processes are diverse
mechanical and physical processes. To solve its main problem, the meteorology must seek
help from the mechanics and the physics, which it already have sought help from these
sciences to solve special problems. Among the leading men for the application of the
principles of the mechanics to atmospheric motion we can with honour mention two
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Norwegian scientists, Guldberg and Mohn. And the more restrict application of the physics, in
particular principles of thermodynamics on evaporation and condensation phenomena in the
atmosphere, is due to Herz, v. Bezold and others. It is the way of these scientists that must be
continued. The principles, which they have applied in the treatment of specialised ideal cases
or simple average conditions, must be brought to application on all real conditions in all their
seemingly hopeless complexity.
All know the physics. It has to a large degree solved its problems of prognosis. In particular
with the two main laws of thermodynamics, the famous principles of the conservation of
energy and the growth of entropy, we might, in connection with the known laws for the
properties of the air and humidity, under changing conditions decide how an air mass will
change temperature, release the water it contains, or take up humidity, when opportunity is
present.
Mechanics might on the other hand be rather unknown for many, and I will therefore handle it
a little closer. Its task is to describe those motions which we observe in nature, and it has
solved its problem of prognoses more completely than any other natural science. Due to
thinkers like Archimedes, Galilei and Newton and a long row of followers of these great
spirits, we have got the experience about earlier observed motion laid down in a system of
mathematical formulas which allow us to calculate the future motion of a system when its
state at present is known.
What importance it has for a science, when the principles of mechanics are applied. The
history of astronomy gives the best testimony. During thousands of years, the astronomy
stood in a similar position as the meteorology in our days. The astronomers followed with
care the path of the stars on the sky, and they succeeded also to some extent to make
prognoses, e.g. to predict eclipses. Then Newton brought the principles of mechanics to
application on the motion of astronomical objects. The result from this is modern astronomy
with its undefeated prognoses that all of us know about. It predicts not only the day for an
eclipse, but also minute and second for its start and termination. And it can calculate
constellations, which our successors will see thousands of years in the future, or as our
ancestors have seen thousands of years in the past.
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The mechanics is now completely developed to, together with physics, take the lead in
theoretical meteorological research. In the days of Newton this was not the case. True enough,
under his hands the principles of mechanics got the form which they have kept ever since. But
the forms for the application of these principles were not yet found for more complicated
cases. It was the great mathematician Euler who one and a half century ago thought us to
bring the principles of mechanics to application on motion in fluids and air masses. The new
branch of mechanics, the hydromechanics, which then started, has later had a rich
development, and many examples could be given on its high position as a prognostic science.
I will give one such, an example of prognoses of the finest kind, the prediction of phenomena
nobody earlier knew about. I am referring to a study of a Norwegian scientist, my late father,
professor C.A. Bjerknes in Kristiania. From Eulers hydrodynamic equations, he has derived a
world of phenomena which exist in motions of fluids, and which have a remarkable similarity
with electrical and magnetic phenomena. The results of his calculation he has later verified
with experiments, and in hundreds of different experiments his pre-calculations have been
proven to the point.
When I mention these studies, it has a special reason. It is, to be precise, through them I have
been brought to the meteorology, without my knowledge and my will, I might nearly say. The
relationship is the following: The hydrodynamical scientists have until now for the most part
kept themselves within a very narrow area. To obtain problems for which the solution do not
meet large mathematical difficulties, one has generally thought that the fluid is provided with
particularly simple properties, in assuming that that its density should depend on its pressure
only. When this assumption is made, then a famous law of Helmholtz is valid, that the
vortices in the fluid are eternal. A mass of fluid which once is curling, will always continue to
curl, and a mass of fluid which does not curl, will never do so. This result seems to stand in
the most unreconciled struggle with the eternal formation and the eternal termination of
vortices in the atmosphere. It seems like this paradox has paralysed initiative from the
hydrodynamicists and prevented them from bringing the principles of hydrodynamics to full
scale application on atmospheric motion. With my trials to generalise the results of my father,
I was forced beyond the area where the hydrodynamicists have remained until now. I had to
consider fluids where the density not exclusively depends on pressure. Then I found, instead
of Helmhltz’ sentences on conservation of vortices, several sentences about the origin and
termination of vortices. I soon understood, that these sentences, which I had developed for
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quite different purposes, contain the precise hydrodynamic formulation of the principles for
formation of vortices in the atmosphere. These sentences have a surprisingly simple and neat
appearance. They bring the formation of vortices to two surfaces in the atmosphere, which
might be found with observations with barometer, thermometer and hygrometer, i.e. surfaces
for constant pressure and surfaces for constant specific volume, isosteric surfaces. The
formation of vortices takes place around the axes made by crossing-lines of the surfaces, and
it is more intensive, the more they cross each other, and weaker the more they follow without
crossing each other.
I have never been a practical meteorologist myself. I would probably be standing just with
results of pure theoretical nature, if I had not found a collaborator in a student, J.W.
Sandstrøm, who fully possessed the technique of meteorologists. What I in the following will
write about, is the result of his and my common work with the mentioned sentences about
formation of vortices as the first starting-point.
V. Treatment of observations from higher layers of the air
The methods derived from this cooperation (explained earlier) will already be needed at the
first preliminary treatment of the observations from higher levels of the air. All of us
immediately realise, that even with the most extensive observation system, direct observations
might just be obtained from a few points in the atmosphere. As they might exist without
observation handling, they will not provide any image of the state of the atmosphere
whatsoever. This image must be constructed on the basis of scattered observations with help
of mechanical and physical laws. Until now this task has only been related to the state of the
atmosphere in one plane only, the surface of the earth. Anyone realise, however, the increased
complexity of the task when the state at all heights is included. In addition, the sparse
availability of direct observations aloft makes it necessary to exploit their entire content to the
greatest possible extent. With knowledge of law connections between the different parameters
of the observations, this should take place in such a way that quantities not directly observed,
are computed as much as possible.
An example will illustrate what might be obtained along these lines. From the mentioned
hydrodynamic sentences Sandstrøm has derived e.g. the following result: Suppose that the
wind down at the surface has the same direction as the drift of the clouds, but that the clouds
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move faster than the wind. If I place myself with the wind in my back, the air layer between
the clouds and the surface will be warmer on my right side than on my left side.
This result is also derived mathematically, and it shows to be correct in all cases where we,
with help of kites and balloon observations, have had the opportunity to check its correctness.
One example all will understand: Above our heads there normally is a rapid flow towards
east. If I look towards east, I have south to the right, and all know, that the air temperature
towards south will normally be higher than towards north. During the exceptionally warm
summer two years ago, it was, however, warmer over mid Sweden than over Germany. Over
mid Sweden there was an anticyclone, and the flow aloft was towards west above southern
Sweden.
And note that this law from Sandstrøm is not qualitative only, but also quantitative. It allows
us, from observations of the drift of the clouds, to draw isotherms for the mean temperature of
deep air layers in the same way as isotherms for the surface are drawn from observations with
thermometers. A similar law exists for air pressure in such a way that isobar maps for higher
levels might be drawn on the basis of observations of the drift of the clouds, in the same way
as done for the surface from barometer readings.
These laws are only examples on how the observation material might be extended by use of
physical relations between the different parameters. In this way a rather complete picture of
the immediate state of the atmosphere can be constructed from scattered observations. The
methods, on which this will be completed, are already nearly fully developed, also in practical
terms, and can be implemented at any time. This will be realized from the following:
Suppose that the suggested observation system already was organised. The observations must
then first be treated preliminary at the observation site, for then to be telegraphed to a central
bureau. When those tables, to be used at a station in question, are developed, the preliminary
treatment of results from a kite trip, will not take more than half an hour to one hour, and the
handling of the cloud drift observations will take considerably less time. After this treatment,
the result might be concentrated in a few numbers, on which agreement is made in advance.
These numbers are telegraphed in, and from them a system of maps is drawn at the central
bureau, displaying the state of the atmosphere from layer to layer to the highest level where
observations exist. These maps can be ready at the latest half an hour after the arrival of the
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last telegram. And if one hour is spent for the collection of the telegrams, then two or three
hours after the ending of the last kite trip, the diagnosis of the state of the atmosphere will be
established at the central bureau.
VI. Rational prediction of the weather
When we have reached so far, the last and primary question turns up: Will we on this basis be
able to predict the weather in a better way than presently?
The answer can not be doubted. Even if the present method of the meteorology, to predict
after marks (precursors as explained earlier) is maintained, the result must definitely become
better because of the availability of a much richer sample of marks, out of which those most
characteristic can be used. We might as an example again look at the winter storms in
Finmark. Judged on all, it is extremely likely that certain symptoms of a storm in development
will be noticed at en earlier stage aloft than at the surface. With sufficient experience about
the significance of the last symptoms, storm warnings could be issued with far better
confidence, and at an earlier stage, so they do not arrive too late to be of any use.
Observations along the coast of Norway, partly of the height and the drift of the clouds and
partly, if possible, with meteorological kites, or instead maybe observations from selected
mountain tops, certainly would have a great importance, also if it turned out impossible to
extend the observation system to the ocean.
But when I here presume that the observation material exists in its completeness, the
possibility for quite new methods to predict the weather is uncovered. Instead of predicting
the weather after marks, we must be able to predict after laws, the laws after which the
atmospheric processes develop.
If it is true, as all men thinking scientifically believe, that the future state of the atmosphere
develops by laws from the present state, then the precondition to predict the future weather is
partly knowledge of the present state of the atmosphere and partly knowledge of the laws after
which the state changes. The question is if we have the necessary knowledge about these
laws. It is impossible in this moment to answer the question definitively. Our knowledge
might have shortcomings that we do not know about. But as far as the question might be
considered at this time, it must be answered with yes.
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The meteorology itself can only provide an approximate message about the laws of the
atmospheric processes. Like we watch them act before our eyes, their nature is too disordered
in order to be discovered.
But they have a mechanical and physical nature, and at our tests with falling objects and
pendulums and with experiments in our laboratories of the properties of the air masses and
moisture, we have studied clean conditions for each of the processes which in the atmosphere
acts with such confusing links to each other. For each of them scientists in mechanics and
physics can set up one or several equations. In this way the question of sufficient knowledge
about the atmospheric processes is reduced to a mathematical question.
Those who at school have solved exercises with help of equations, will know that an exercise
can be solved if there are as many equations as there are unknown variables to calculate. In
the atmosphere we have to calculate three motion components to denote the direction and the
speed of the wind, and in addition the air pressure, density, temperature and humidity,
altogether seven variables. For the calculation of these we can set up four equations from
hydrodynamics and three from thermodynamics, seven equations altogether. Thus the
problem is determined mathematically, and judged on all, we are in possession of the
complete knowledge of the laws after which one atmospheric state develops from the other.
But as the case often is for public laws, as simple as each law in its principle might be
separately, the interpretation in the real complicated cases, offered by life, might be connected
with the greatest difficulty. The law interpretation is here a mathematical exercise, and anyone
realize its enormous dimension: at a given time these seven quantities, which depend on each
other mutually in a complicated way, must be calculated for every single point of the
atmosphere.
An exercise of this nature, the mathematicians refer to as integration of a system of partial
differential equations. To a large extent, our countryman Sophus Lie has gained his fame for
fine methods to solve problems of this kind. But all such methods will here fail, if we try to go
the usual way for mathematicians and demand the exact solution. For the exact solution
would, however, be of no use. It would contain all details, down to the description of each
whirlwind that develop on a street corner, and in such a magnitude of details none would be
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able to orient. What we want to know is practical average results only. Fortunately, in the
maps on the state of the atmosphere, that we to have to start from, the meaningless details are
already wiped out. And if we think our task in this form: on basis of the maps, that gives the
mean state of the atmosphere today, to construct similar maps that presents the mean state
tomorrow, then nothing overwhelmingly frightening is any longer included in the task. The
great basic principle of mathematical thinking might then be applied without being dependent
of special hard-developed, troublesome methods, which just are applicable on limited areas,
and which are the possession of a few specialists only.
Mathematics is the least popular of all sciences. The mathematical thinking is, however, in its
character not at all different from common sound thinking, and the great principle of progress
in mathematics is a principle owned by every man. It is simply this: what I fail to complete in
one turn, I will try to complete in two or several turns. In mathematics this is carried out to its
utmost consequence. We might imagine a supernatural intelligence, which in one single
operation of thoughts could manage to solve any mathematical exercise. But our weak brains
are not able to do this. Our only way out is to resolve such a complicated operation of
thoughts in a series of simpler, which each can be carried out by our brains. This principle all
of us know from the normal rules for addition and multiplication of numbers with several
digits. And each time a mathematician says he has solved an exercise, this means that he has
succeeded to resolve an operation of thoughts in a series of simpler calculable operations of
thoughts, which all are known. In the exercise we have in front of us, what counts is to find a
line, along which the total, overwhelming task might be divided into several more obtainable
exercises. Such a line of partition can also be given. It follows the borderline between the
mechanical and physical processes that the atmospheric processes are made up of. It is easier
to understand this when I immediately give a scheme to follow for mathematical calculation
in advance of future weather.
I presume that in front of me I have the maps, which the observations have given, and which
show the motion of the air, its density, pressure, temperature, and humidity at 12 am in all
heights over a large part of the earth. I then assume that temperature and the humidity are
unchanged until 1 pm. Under this assumption I can draw new maps that display a certain new
state of motion and a certain new distribution of density and pressure at 1 pm. The maps will
then with a large degree of approximation give the real state of motion at 1 pm, but they give
somewhat distorted distributions of density, pressure, temperature, and humidity.
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The next operation then consists in calculation of the correct distributions of these quantities
at 1 pm. This might be done as a pure physical problem, without once more bringing in the
motion. With knowledge of the work that air masses have done during the computed motion,
and with knowledge of the amount of heat gained though radiation from the sun or lost from
outgoing radiation, the change that the temperature and humidity experience between 12 am
and 1 pm is calculated, and from this again the correct density and pressure at 1 pm.
With these maps as a start, after the same scheme I can construct those maps which show the
state of the air at 2 pm, then at 3 pm, 4 pm etc.
When we proceed in this way, on no point we will meet operations which can not be carried
out. As soon as the necessary tables and graphical means are brought forward, then it is my
believe that the operations will turn up so easy to perform, that for that matter nothing will
stand hindering in the road for practical application for the issue of daily weather forecasts.
With this I have not said that the method right away will be mature for this application. But
the scientific study of the development of one atmospheric state from the other must
necessarily take this kind of procedure or a nearly related one. Only such a study might lead
us on the track of the deepest lying and most reliable marks of the weather, and directly or
indirectly the mechanical and physical study of the track of the atmospheric processes will
benefit practical weather prediction accordingly.
How far we might reach in the direction of practical weather prediction, naturally none in
advance can have any certain opinion of. But there is nothing unlikely in the assumption, that
the introduction of exact methods in the end will cause as large a transformation in
meteorology as it caused in astronomy. However, we must not expect a sudden revolution.
The problem solved by Newton, despite its cosmic dimensions, was in its nature a very simple
problem, so it could become the task of one person only to carry it all out. The solution of the
main problem in meteorology demands, however, according to its nature participation from
the many, and the methods must develop successively under steady interaction between
theory and experience. But when this development is competed, there is nothing unlikely
therein, that as the astronomers years in advance predicts minutes and seconds for eclipses,
the meteorology days or weeks in advance will predict the day and the time of the day of a
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major change in the weather. And as the astronomers compute the values of the orbit
constants of the planets thousands of years into the future, we might once experience that the
meteorologists will predict the character of the seasons, cold or warm, dry or humid summer;
mild or strong, calm or stormy winter.
Not the least, the solution of in particular the last problem, on predictions for long time, will
depend on the extension of the meteorological observations to the ocean, which covers four
fifths of the surface of the earth, and which stores sun energy to a degree that neither the land
surface or the air can do. Studies of the great work machines, for example such as that
bringing forward the storms in Finmark, must necessarily be brought in the foreground.
Accordingly, we have a special reason to expect much from the natural cooperation between
meteorological and the hydrographical research. This cooperation is also natural because the
theoretical methods, which I here have developed for application on the air, will have
precisely the same application on the ocean.
The prediction of the alteration of the state of the ocean is a problem of the same nature as for
weather prediction, and will demand its solution, not just because it is included as a necessary
step in weather prediction for longer periods, but also for its own sake. It is not to wonder,
that a fishing community like our, depending on the puzzles of the ocean, can misjudge a
phenomena like the seal invasion at the coast of Finmark, which judged from all just has been
a symptom on a change in the state of the ocean, explaining the reason for the absence of the
fish. But full trust the science first will obtain and full use it first will give, when it solves the
problem of prognosis also for the ocean, and predicts the changed states, so that the people
might take their precautions accordingly.
The circumstance, that the problems of prognosis for air and ocean theoretically is so closely
related, and in practice so closely connected to each other, will ease the solution of both. And
the large state-economical and philanthropic interests, which are tied to their solution, will
always be a spur of invaluable importance for researchers in their continuous work.
2 June 2009
Sigbjørn Grønås
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